Known in the present state of the art is a tool of gear form for finishing bevel gears (U.S. Pat. No. 2,256,586) which meshes with a bevel gear with its axis offset from and angularly disposed to the axis of the bevel gear to be produced. The method of determination of tooth profile modification involves matching the angle of tooth profile, the tooth spiral angle, and the tooth pitch line with respective parameters of tooth surfaces of the gear to be machined. Employment of such a tool for gear finishing enables the velocity of relative sliding movement between the machining surface and the surface being machined; the normal component of the cutting force; the reduced curvature radii of the tool surfaces contacting the gear to be machined, etc., to be regulated lengthwise on the tooth pitch line only. In other points over the tooth surface, these parameters, however cannot be regulated. As a result, unpredictable departures of tooth surfaces from true profile can be encountered after gear finishing.
According to another prior-art method for determination of gear tooth modification (SU, A, 199,643), the surface of the tool gear tooth envelops that of the gear tooth being machined, and a linear contact is maintained as the tool gear meshes with the gear to be machined. In the course of machining, the tool gear and the gear to be machined are rotated with constant angular velocities (in synchronism).
However, this prior-art method also fails to provide the requisite machining accuracy. During gear honing, lapping, burnishing or other kinds of abrasive finish treatment, the process of metal removal from each of the surfaces machined is similar to abrasive wearing. In the general case, the amount of linear wear can be determined by the following relationship (cf., a textbook "Abrasive Wearing" by N. N. Khrushchev et al, "Nauka" Publishers, 1970, Moscow, p. 96, in Russian): EQU .DELTA.l=cp.DELTA.S (1)
wherein:
l--linear wear on the gear blank machined, measured in meters; PA1 c--proportionality factor which is constant for a given pair of friction members; PA1 p--normal component of the cutting force, measured in Newtons; PA1 .DELTA.S--friction length, measured in meters. PA1 .DELTA.p--the requisite changes in the normal component of the cutting force, measured in Newtons; PA1 G--the rigidity where the torsional rigidity is the torque applied to the shaft divided by the turning angle of the driveshaft as a result of the twisting of all shafts of the kinematic train of an arrangement providing for synchronous rotation of the gear blank and the tool gear as reduced to the tool gear axis, measured in newton meter/radian; PA1 V.sub.s --the velocity of relative sliding motion between the machining surface and the surface being machined, measured in meters/second; PA1 V.sub.r --the velocity of movement of the contact point along the surface being machined, measured in meters/second.
In the case of bevel gear honing using a tool of gear form, the friction length .DELTA.S will be directly proportional to the velocity V.sub.S (measured in meters/second) of relative sliding motion between the machining surface and the surface being machined and inversely proportional to the velocity V.sub.r (measured in meters/second) of movement of the contact point along the surface being machined. Then: ##EQU2##
But the values of V.sub.s and V.sub.r, hence .DELTA.l will varied at different points of the tooth surface, resulting in nonuniform removal of stock from different portion of the gear blank tooth surface and in uneven wear of the tool gear tooth surfaces, which reduces machining accuracy and tool service life.
The closest to the herein proposed invention is a method for determination of longitudinal and profile modification of tooth surfaces of a tool gear which linearly meshes with a gear to be machined (cf., a textbook "Machine Tool Design" by I. I. Semenchenko et al, "Mashgiz" Publishers, 1963, p. 792-794, in Russian), wherein gear teeth of required shape are obtained due to employment of a tool gear whose tooth profile surface have been properly corrected through modification. The profile of tool gear teeth is modified during tool gear manufacture, to suit the deviations of gear teeth resulting from gear finishing. A requisite profile of the tool gear teeth is determined experimentally on the basis of testing the gears after machining and taking their measurements. This prior-art method involves manufacturing a certain number of test lots of gear blanks produced by tool gears featuring periodic modification of the profile of their teeth after successive finishing operation. Since each type of gear may have its own kind of modification, the above-discussed prior-art method proves to be expensive and will be commercially successful only in mass or large-lot gear manufacture.